: com net

: (f(2010

2. The Following User Says Thank You to For This Useful Post:

(12-15-2014)

3. : (f(2010

$\dpi{150}&space;\fn_cm&space;\\&space;\because&space;\&space;{\color{Blue}&space;f\left&space;(&space;x+1&space;\right&space;)&space;=\frac{1+f\left&space;(&space;x&space;\right&space;)}{1-f\left&space;(&space;x&space;\right&space;)}}&space;\\&space;\\&space;\therefore&space;\&space;{\color{Blue}&space;f\left&space;(&space;2&space;\right&space;)=\frac{1+f\left&space;(&space;1\right&space;)}{1-f\left&space;(&space;1&space;\right&space;)}}&space;\\&space;\\&space;\therefore&space;\&space;{\color{Blue}f\left&space;(&space;3&space;\right&space;)=\frac{1+f\left&space;(&space;2&space;\right&space;)}{1-f\left&space;(&space;2&space;\right&space;)}&space;}=\frac{\left&space;(1+\frac{1+f\left&space;(&space;1&space;\right&space;)}{1-f\left&space;(&space;1&space;\right&space;)}&space;\right&space;)}{\left&space;(1-\frac{1+f\left&space;(&space;1&space;\right&space;)&space;}{1-f\left&space;(&space;1&space;\right&space;)}&space;\right&space;)}&space;.\frac{\left&space;(&space;1-f\left&space;(&space;1&space;\right&space;)&space;\right&space;)}{\left&space;(&space;1-f\left&space;(&space;1&space;\right&space;)&space;\right&space;)}$

$\dpi{150}&space;\fn_cm&space;\\&space;\therefore&space;\&space;{\color{Blue}&space;f\left&space;(&space;3&space;\right&space;)}=\frac{\left&space;(&space;1-f\left&space;(&space;1&space;\right&space;)+1+f\left&space;(&space;1&space;\right&space;)&space;\right&space;)}{\left&space;(1-f\left&space;(&space;1&space;\right&space;)&space;-1-f\left&space;(&space;1&space;\right&space;)&space;\right&space;)}=\frac{2}{-2f\left&space;(&space;1&space;\right&space;)}&space;\\&space;\\&space;\therefore&space;{\color{Blue}&space;\&space;f\left&space;(&space;3&space;\right&space;)}={\color{Blue}&space;\frac{-1}{f\left&space;(&space;1&space;\right&space;)}}$

:

$\dpi{150}&space;\fn_cm&space;\\&space;{\color{Blue}&space;f\left&space;(&space;5&space;\right&space;)=\frac{-1}{f\left&space;(&space;3&space;\right&space;)}}&space;\\&space;\\&space;\therefore&space;\&space;\&space;{\color{Blue}&space;f\left&space;(&space;5&space;\right&space;)=\frac{-1}{\left&space;(&space;\frac{-1}{f\left&space;(&space;1&space;\right&space;)}&space;\right&space;)}}\rightarrow&space;{\color{Blue}&space;f\left&space;(&space;5&space;\right&space;)=f\left&space;(&space;1&space;\right&space;)}$

:

$\dpi{150}&space;\fn_cm&space;\\&space;{\color{Blue}&space;f\left&space;(&space;9&space;\right&space;)=f\left&space;(&space;5&space;\right&space;)}&space;\\&space;but&space;\&space;\&space;{\color{Blue}&space;f\left&space;(&space;5&space;\right&space;)=f\left&space;(&space;1&space;\right&space;)}&space;\\&space;\therefore&space;\&space;\&space;{\color{Blue}&space;f\left&space;(&space;1&space;\right&space;)=f\left&space;(&space;5&space;\right&space;)=f\left&space;(&space;9&space;\right&space;)}$

:

$\dpi{150}&space;\fn_cm&space;\\&space;{\color{Blue}&space;f\left&space;(&space;1&space;\right&space;)=f\left&space;(&space;5&space;\right&space;)=f\left&space;(&space;9&space;\right&space;)=f\left&space;(&space;13&space;\right&space;)=f\left&space;(&space;17&space;\right&space;)=...........}&space;\\&space;\\&space;\therefore&space;\&space;\&space;{\color{Blue}&space;f\left&space;(1+4m&space;\right&space;)=f\left&space;(&space;1&space;\right&space;)&space;\&space;\&space;\forall&space;\&space;m\in&space;N}&space;\\&space;\\&space;\because&space;\&space;\&space;{\color{Blue}&space;f\left&space;(&space;2009&space;\right&space;)=f\left&space;(&space;1+2008&space;\right&space;)=f\left&space;(&space;1+4\left&space;(&space;502&space;\right&space;)&space;\right&space;)&space;\&space;:&space;\&space;502\in&space;N}&space;\\&space;\\&space;\therefore&space;{\color{Blue}&space;\&space;\&space;f\left&space;(&space;2009&space;\right&space;)=f\left&space;(&space;1&space;\right&space;)}&space;\\&space;\\&space;\therefore&space;\&space;\&space;{\color{Blue}&space;f\left&space;(&space;2010&space;\right&space;)=\frac{1+f\left&space;(&space;2009&space;\right&space;)}{1-f\left&space;(&space;2009&space;\right&space;)}=\frac{1+f\left&space;(&space;1&space;\right&space;)}{1-f\left&space;(&space;1&space;\right&space;)}=\frac{1+2}{1-2}}$

$\dpi{150}&space;\fn_cm&space;\therefore&space;\&space;\&space;{\color{Blue}&space;f\left&space;(&space;2010&space;\right&space;)=-3}$

4. The Following 2 Users Say Thank You to For This Useful Post:

(12-15-2014),  (12-16-2014)

: 1 (0 1 )